Question

Solve the following equation $3\left( {n - 5} \right) = 21$ .

Answer 1

Hint-In this question, we use the property of basic algebraic equations. Like If we shift any number from one side of the equation to the other side of the equation so the nature of mathematical operation becomes changed. Example; 2x+3=5 if we shift 3 on other side of equation so $2 \times x = 5 - 3 \Rightarrow 2 \times x = 2$ and if we shift 2 on other side so multiply operation changes to divide $2 \times x = 2 \Rightarrow x = \dfrac{2}{2} \Rightarrow x = 1$ .
Complete step-by-step solution -
Given, $3\left( {n - 5} \right) = 21$
Now, multiply by 3 in brackets.
$ \Rightarrow 3n - 15 = 21$
We have to use the basic algebraic equation, If we shift 15 to the other side of the equation so the nature of mathematical operation of 15 number changes, subtraction to addition.
\[
   \Rightarrow 3n = 21 + 15 \\
   \Rightarrow 3n = 36 \\
   \Rightarrow 3 \times n = 36 \\
 \]
Now, if we shift 3 to the other side of the equation , the nature of mathematical operation of 3 changes, multiplication to division.
\[
   \Rightarrow n = \dfrac{{36}}{3} \\
   \Rightarrow n = 12 \\
\]
So, the value of n is 12.

Note-We can solve the above question by two different ways, First way we already mention above and in second way, we know 3 is multiply with (n-5) so if we shift 3 on other side of equation then the nature of mathematical operation of 3 changes, multiplication to division and then shift 5 to other side of equation so the answer is $n = \dfrac{{21}}{3} + 5 = 7 + 5 = 12$ .